## timeline of calculus

Calculus was developed as a way to calculate areas and volumes of shapes that are not easy to figure using simple math. Differential calculus studies the derivative, which calculates the slope of a line tangent to the function. The slope of the line shows the rate of change in the line. If the line represents velocity, the slope shows the change in velocity, or acceleration.

Integral calculus studies the “anti-derivative”, which calculates the original function from a derivative. Integrals can be used to calculate the area under a curve, which can represent area or volume of a curved shape or other complex problems such as speed/time calculations with a variable speed component.

The “fundamental theorem of calculus” states that derivatives and integrals and the processes associated with finding them are essentially the inverse of each other. This concept was developed simultaneously and independently by both Newton and Leibniz.

-1820 – Moscow papyrus, calculations of volume – Egypt

-0450 – problems based on infinity – **Zeno** (of Elea)

-0370 – method of exhaustion – **Eudoxus** and Antiphon

-0225 – first known summation of an infinite series – **Archimedes**

0263 – Cavalieri’s principle (“Nine Chapters”) – Liu Hui

0499 – trigonometry and sum of cubes (volume) – **Aryabhata**

1021 – Alhazen’s problem (“Book of Optics”), integrals of fourth degree – **Alhazen**

1150 – spherical trigonometry and Rolle’s theorem – Bhaskara

1400 – infinite series expansions – Madhava

1615 – infinitesimally small geometric quantities – **Kepler**

1635 – theory of indivisibles – Cavalieri

16xx – motion with variable speed – Torricelli and Barrow

1679 – maxima, minima and tangents – **Fermat**

1684 – infinitesimal calculus – **Leibniz**

1693 – fluxion calculus – **Newton**

1825 – integral theorem – **Cauchy**